@article{DialloKuleshHolschneideretal.2005,
  author    = {Diallo, Mamadou Sanou and Kulesh, Michail and Holschneider, Matthias and Scherbaum, Frank},
  title     = {Instantaneous polarization attributes in the time-frequency domain and wavefield separation},
  issn      = {0016-8025},
  year      = {2005},
  abstract  = {We introduce a method of wavefield separation from multicomponent data sets based on the use of the continuous wavelet transform. Our method is a further generalization of the approach proposed by Morozov and Smithson, in that by using the continuous wavelet transform, we can achieve a better separation of wave types by designing the filter in the time-frequency domain. Furthermore, using the instantaneous polarization attributes defined in the wavelet domain, we show how to construct filters tailored to separate different wave types (elliptically or linearly polarized), followed by an inverse wavelet transform to obtain the desired wave type in the time domain. Using synthetic and experimental data, we show how the present method can be used for wavefield separation},
  language  = {en}
}
@article{HolschneiderDialloKuleshetal.2005,
  author    = {Holschneider, Matthias and Diallo, Mamadou Sanou and Kulesh, Michail and Ohrnberger, Matthias and Luck, E. and Scherbaum, Frank},
  title     = {Characterization of dispersive surface waves using continuous wavelet transforms},
  issn      = {0956-540X},
  year      = {2005},
  abstract  = {In this paper, we propose a method of surface waves characterization based on the deformation of the wavelet transform of the analysed signal. An estimate of the phase velocity (the group velocity) and the attenuation coefficient is carried out using a model-based approach to determine the propagation operator in the wavelet domain, which depends nonlinearly on a set of unknown parameters. These parameters explicitly define the phase velocity, the group velocity and the attenuation. Under the assumption that the difference between waveforms observed at a couple of stations is solely due to the dispersion characteristics and the intrinsic attenuation of the medium, we then seek to find the set of unknown parameters of this model. Finding the model parameters turns out to be that of an optimization problem, which is solved through the minimization of an appropriately defined cost function. We show that, unlike time-frequency methods that exploit only the square modulus of the transform, we can achieve a complete characterization of surface waves in a dispersive and attenuating medium. Using both synthetic examples and experimental data, we also show that it is in principle possible to separate different modes in both the time domain and the frequency domain},
  language  = {en}
}
@article{KuleshHolschneiderDialloetal.2005,
  author    = {Kulesh, Michail and Holschneider, Matthias and Diallo, Mamadou Sanou and Xie, Q. and Scherbaum, Frank},
  title     = {Modeling of wave dispersion using continuous wavelet transforms},
  issn      = {0033-4553},
  year      = {2005},
  abstract  = {In the estimate of dispersion with the help of wavelet analysis considerable emphasis has been put on the extraction of the group velocity using the modulus of the wavelet transform. In this paper we give an asymptotic expression of the full propagator in wavelet space that comprises the phase velocity as well. This operator establishes a relationship between the observed signals at two different stations during wave propagation in a dispersive and attenuating medium. Numerical and experimental examples are presented to show that the method accurately models seismic wave dispersion and attenuation},
  language  = {en}
}